Flack parameter

The definition of the Flack parameter (Flack, 1983 Bemadinelli and Flack, 1985) is a special case of Equation 7.8 ... 

In acentric space groups and in the presence of heavy atoms such as osmium it should be possible to determine the absolute stmcture and the absolute structure parameter needs to be checked (.1st file). The Flack parameter x (Flack, 1983) is refined to 0.54(2). This could mean that the absolute structure is wrong and space group P3 is the correct one instead of P32 and/or that there is some additional racemic twinning. This can be tested by changing the TWIN and BASF command lines ... 

The absolute configurations of daphmalenines A (20) and B (21) were determined on X-ray diffraction by using the Flack parameter and computational methods, respectively. Daphnioldhamine A (22) is the first Daphniphyllum alkaloid with transannular effect and is easily tautomerized imder acidic or alkaline conditions (Figure 5). 

To determine more simply the AC without the measurement of the Bijvoet pairs, the Flack parameter x was introduced as formulated in equation (5)... 

If the parameter x = 0 is obtained, the AC tentatively assigned is correct. On the other hand, if x = 1, the opposite AC is assigned. Thus, the simple method using the Flack parameter has become more popular these days. Recently, a new probabilistic method was introduced, where the measurement of Bijvoet pairs is required." ... 

Inconclusive results are likely to be obtained for light-atom structures because of the low amount of anomalous scattering, as well as for nearly centrosymmetric structures, especially if the heavy atoms are distributed nearly centrosymmetrically 27. In the latter case the rj value may even refine to a false minimum with a deceptively small error estimate59. This led to the development of an alternative test by Flack which also overcomes these problems39-59. Flack introduced an absolute structure parameter x, which is defined by structure factor equation 12, and which is treated as a variable in the least-squares refinement. 

Today, structural calculation from the diffractogram allows the Flack s parameter to be determined automatically. This is equal, or very close, to zero if the absolute configuration attributed to the molecule is correct, and is equal to unity in the case of the opposite configuration. It is equal or close to 0.5 if the two configurations are present in equal amounts in the crystal. 

The structure of the major diastereomer 4.18a in sample 1 was determined by X-ray diffraction analysis. Complex 4.18a crystallizes in the chiral space group P2i, a view of the complex is shown in Figure 4.10. The absolute configuration of the molecules in the structure was confirmed by refining the Flack s x parameter and was equal to —0.02(1), attesting to the enantiopure character of the crystal.This complex possesses planar chirality and the absolute configuration of the metal centres in the cationic species... 

For every atom in the model that is located on a general position in the unit cell, there are three atomic coordinates and one or six atomic displacement parameters (one for isotropic, six for anisotropic models) to be refined. In addition there is one overall scale factor per structure (osf, or the first free variable in SHELXL see Section 2.7) and possibly several additional scale factors, like tbe batch scale factors in the refinement of twirmed structures, the Flack-x parameter for non-centrosymmetric structures, one parameter for extinction, etc. In addition to the overall scale factor, SHELXL allows for up to 98 additional free variables to be refined independently. These variables can be tied to site occupancy factors (see Chapter 5) and a variety of other parameters such as interatomic distances. 

A value of 0.5 for the Flack-x parameter points to a 50 50 twin, corresponding to a value of 0.5 for the BASF. Frequently, however, a starting value of 0.5 for free variables or batch scale factors corresponds to a pseudo-minimum. It is better to start with values slightly above or below 0.5, for example 0.4 or 0.6. 

The only remaining unsatisfactory feature is the value of the Flack x parameter. It is not possible to determine the absolute stmcture with certainty. We also tried the feature in SHELXL for introducing additional racemic twinning, so that we... 

Such a behaviour of the electron density distribution agrees well with the results of X-ray diffraction measurements (Kubel, Flack and Ivon, 1987) and can be explained qualitatively making use of the covalency parameters and the densities of f2g and states. In TiC and other carbides there are eight electrons per unit cell, and the electron density symmetry is determined mainly by C2p electrons and the admixture of metal d states, which have mainly the symmetry component. As the number of valence electrons in carbides increases, the contributions of the t2g metal states also increase. Such an effect takes place when going from carbides to nitrides. However, in all cases there are no local maxima in the electron density distribution in the metal-nonmetal direction, which would be expected taking into account covalency. Inside nonmetal atomic spheres the distribution of the valence electrons is close to spherical, and the presence of the covalent metal-nonmetal bonds is revealed in the deformation of electron density in the direction away from the centres of metalloid atoms to the metal atoms, see Fig. 3.4. 

For a judicious control of the macroscopic properties of polymer blends, phase morphology constitutes a key parameter for many specific applications. The blending process of immiscible polymers in the melt state results in a heterogeneous morphology that is characterized by the shape, the size, and the distribution of the component phases. Depending on the composition, the homopolymer characteristics and the processing conditions used to mix them, two main types of morphologies are obtained, a dispersed type (a particle can be of any shape rod, platelet, flacks, disc, sphere, etc.) or a co-continuous one. 

F Kubel, HD Flack, K Yvon. Electron densities in VN. I. High-precision x-ray-diffraction determination of the valence-electron density distribution and atomic displacement parameters. Phys Rev B 36 1415, 1987. 

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